I don't think a game can physically destroy a graphics card. Graphics cards have security features inside that will lock the card if the temperature on the GPU becomes too high.

If you run the card with too high settings the card will lock up frequently, but it will not permanently destroy the card. If you set the graphics detail too high in games on a slow graphics card then you will see a very low fps (frames per second). The game will feel laggy and be unplayable.

Graphics cards have a life span so if you run on it for some years the components will start to fail. E. g. I have used up 2 ATI HD5970. Each lasted a little less than 3 years before I got artifacts and some lock-ups. The reason was that memory blocks were starting to fail.

An Nvidia 8600GS is a very old card. How long has the card been used prior to you getting it?